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Homework Help: Show that sq. root of 2 to power sq. root of 2 to N converges

  1. Apr 11, 2010 #1
    Show that sq. root of 2 to power sq. root of 2 to .... N converges

    Sq. root of 2^sq root of 2 ^ sq. of 2......N
    Use monotonous convergence theorem to that it converges and determine what it converges to.
     
  2. jcsd
  3. Apr 11, 2010 #2

    Dick

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    Re: Show that sq. root of 2 to power sq. root of 2 to .... N converges

    Your definition of the sequence is ambiguous. Do you mean a_n+1=a_n^sqrt(2) or a_n+1=sqrt(2)^a_n? Try punching out some terms on a calculator of each. One of them doesn't converge. Then tell me what you need to prove about the sequence to use the monotone convergence theorem.
     
  4. Apr 11, 2010 #3
    Re: Show that sq. root of 2 to power sq. root of 2 to .... N converges

    i ment,
    (sq. rt of 2)^(sq. rt of 2)^(sq. rt of 2)^N
     
  5. Apr 11, 2010 #4

    Dick

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    Re: Show that sq. root of 2 to power sq. root of 2 to .... N converges

    sqrt(2)^sqrt(2)^sqrt(2) doesn't mean anything. (sqrt(2)^sqrt(2))^sqrt(2) and sqrt(2)^(sqrt(2)^sqrt(2)) are different. Use parentheses. It's easier if you define a_n+1 in terms of a_n.
     
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